LMFDB - Embedded newform 336.2.bj.g.191.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(95,336)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("336.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.8275904784.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 4x^{4} - 18x^{3} + 45x^{2} - 81x + 81 $ x^8 - 3x^7 + 5x^6 - 6x^5 + 4x^4 - 18x^3 + 45x^2 - 81*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.3
Root			$0.906034 - 1.47618i$ of defining polynomial
Character	$\chi$	$=$	336.191
Dual form			336.2.bj.g.95.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.906034 - 1.47618i) q^{3} +(3.41502 + 1.97166i) q^{5} +(-1.13746 - 2.38876i) q^{7} +(-1.35821 - 2.67493i) q^{9} +O(q^{10})$	\(q+(0.906034 - 1.47618i) q^{3} +(3.41502 + 1.97166i) q^{5} +(-1.13746 - 2.38876i) q^{7} +(-1.35821 - 2.67493i) q^{9} +(1.76424 + 3.05575i) q^{11} +2.00000 q^{13} +(6.00465 - 3.25479i) q^{15} +(-4.35387 + 2.51371i) q^{17} +(-2.63746 - 1.52274i) q^{19} +(-4.55682 - 0.485208i) q^{21} +(0.825391 - 1.42962i) q^{23} +(5.27492 + 9.13642i) q^{25} +(-5.17926 - 0.418627i) q^{27} -6.80257i q^{29} +(1.50000 - 0.866025i) q^{31} +(6.10930 + 0.164282i) q^{33} +(0.825391 - 10.4004i) q^{35} +(-0.637459 + 1.10411i) q^{37} +(1.81207 - 2.95236i) q^{39} -2.16818i q^{41} +0.837253i q^{43} +(0.635769 - 11.8129i) q^{45} +(-2.47617 + 4.28886i) q^{47} +(-4.41238 + 5.43424i) q^{49} +(-0.234071 + 8.70459i) q^{51} +(-8.36737 + 4.83090i) q^{53} +13.9140i q^{55} +(-4.63746 + 2.51371i) q^{57} +(5.06580 + 8.77423i) q^{59} +(5.63746 - 9.76436i) q^{61} +(-4.84488 + 6.28706i) q^{63} +(6.83004 + 3.94333i) q^{65} +(-13.9124 + 8.03231i) q^{67} +(-1.36254 - 2.51371i) q^{69} -10.3585 q^{71} +(3.63746 + 6.30026i) q^{73} +(18.2662 + 0.491189i) q^{75} +(5.29272 - 7.69014i) q^{77} +(4.50000 + 2.59808i) q^{79} +(-5.31055 + 7.26622i) q^{81} -5.17926 q^{83} -19.8248 q^{85} +(-10.0418 - 6.16335i) q^{87} +(-6.23157 - 3.59780i) q^{89} +(-2.27492 - 4.77753i) q^{91} +(0.0806424 - 2.99892i) q^{93} +(-6.00465 - 10.4004i) q^{95} +4.27492 q^{97} +(5.77774 - 8.86957i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{3} + 6 q^{7} - q^{9}+O(q^{10}) $ 8 * q + 3 * q^3 + 6 * q^7 - q^9	$ 8 q + 3 q^{3} + 6 q^{7} - q^{9} + 16 q^{13} - 6 q^{19} - 19 q^{21} + 12 q^{25} + 12 q^{31} - 11 q^{33} + 10 q^{37} + 6 q^{39} - 17 q^{45} + 10 q^{49} - 9 q^{51} - 22 q^{57} + 30 q^{61} - 27 q^{63} - 66 q^{67} - 26 q^{69} + 14 q^{73} + 66 q^{75} + 36 q^{79} + 7 q^{81} - 68 q^{85} - 54 q^{87} + 12 q^{91} + 3 q^{93} + 4 q^{97}+O(q^{100}) $ 8 * q + 3 * q^3 + 6 * q^7 - q^9 + 16 * q^13 - 6 * q^19 - 19 * q^21 + 12 * q^25 + 12 * q^31 - 11 * q^33 + 10 * q^37 + 6 * q^39 - 17 * q^45 + 10 * q^49 - 9 * q^51 - 22 * q^57 + 30 * q^61 - 27 * q^63 - 66 * q^67 - 26 * q^69 + 14 * q^73 + 66 * q^75 + 36 * q^79 + 7 * q^81 - 68 * q^85 - 54 * q^87 + 12 * q^91 + 3 * q^93 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.906034	−	1.47618i	0.523099	−	0.852272i
$3$	0.906034	−	1.47618i	0.523099	−	0.852272i
$4$		0			0
$5$	3.41502	+	1.97166i	1.52724	+	0.881755i	0.999476	+	0.0323665i	$0.0103044\pi$
$5$	3.41502	+	1.97166i	1.52724	+	0.881755i	0.527768	+	0.849388i	$0.323029\pi$
$6$		0			0
$7$	−1.13746	−	2.38876i	−0.429919	−	0.902867i
$7$	−1.13746	−	2.38876i	−0.429919	−	0.902867i
$8$		0			0
$9$	−1.35821	−	2.67493i	−0.452735	−	0.891645i
$10$		0			0
$11$	1.76424	+	3.05575i	0.531938	+	0.921344i	0.999305	+	0.0372805i	$0.0118695\pi$
$11$	1.76424	+	3.05575i	0.531938	+	0.921344i	−0.467367	+	0.884064i	$0.654797\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$	6.00465	−	3.25479i	1.55039	−	0.840383i
$16$		0			0
$17$	−4.35387	+	2.51371i	−1.05597	+	0.609664i	−0.924314	−	0.381632i	$-0.875362\pi$
$17$	−4.35387	+	2.51371i	−1.05597	+	0.609664i	−0.131654	+	0.991296i	$0.542029\pi$
$18$		0			0
$19$	−2.63746	−	1.52274i	−0.605075	−	0.349340i	0.165961	−	0.986132i	$-0.446927\pi$
$19$	−2.63746	−	1.52274i	−0.605075	−	0.349340i	−0.771035	+	0.636792i	$0.780261\pi$
$20$		0			0
$21$	−4.55682	−	0.485208i	−0.994379	−	0.105881i
$22$		0			0
$23$	0.825391	−	1.42962i	0.172106	−	0.298096i	−0.767050	−	0.641587i	$-0.778276\pi$
$23$	0.825391	−	1.42962i	0.172106	−	0.298096i	0.939156	+	0.343491i	$0.111610\pi$
$24$		0			0
$25$	5.27492	+	9.13642i	1.05498	+	1.82728i
$26$		0			0
$27$	−5.17926	−	0.418627i	−0.996749	−	0.0805648i
$28$		0			0
$29$		−	6.80257i		−	1.26320i	−0.775292	−	0.631602i	$-0.782397\pi$
$29$		−	6.80257i		−	1.26320i	0.775292	−	0.631602i	$-0.217603\pi$
$30$		0			0
$31$	1.50000	−	0.866025i	0.269408	−	0.155543i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	1.50000	−	0.866025i	0.269408	−	0.155543i	0.628619	+	0.777714i	$0.283621\pi$
$32$		0			0
$33$	6.10930	+	0.164282i	1.06349	+	0.0285979i
$34$		0			0
$35$	0.825391	−	10.4004i	0.139517	−	1.75798i
$36$		0			0
$37$	−0.637459	+	1.10411i	−0.104798	+	0.181515i	−0.913655	−	0.406489i	$-0.866753\pi$
$37$	−0.637459	+	1.10411i	−0.104798	+	0.181515i	0.808858	+	0.588004i	$0.200086\pi$
$38$		0			0
$39$	1.81207	−	2.95236i	0.290163	−	0.472755i
$40$		0			0
$41$		−	2.16818i		−	0.338612i	−0.985563	−	0.169306i	$-0.945847\pi$
$41$		−	2.16818i		−	0.338612i	0.985563	−	0.169306i	$-0.0541527\pi$
$42$		0			0
$43$			0.837253i			0.127680i	0.997960	+	0.0638400i	$0.0203347\pi$
$43$			0.837253i			0.127680i	−0.997960	+	0.0638400i	$0.979665\pi$
$44$		0			0
$45$	0.635769	−	11.8129i	0.0947749	−	1.76096i
$46$		0			0
$47$	−2.47617	+	4.28886i	−0.361187	+	0.625594i	−0.988156	−	0.153450i	$-0.950962\pi$
$47$	−2.47617	+	4.28886i	−0.361187	+	0.625594i	0.626969	+	0.779044i	$0.284295\pi$
$48$		0			0
$49$	−4.41238	+	5.43424i	−0.630339	+	0.776320i
$50$		0			0
$51$	−0.234071	+	8.70459i	−0.0327765	+	1.21889i
$52$		0			0
$53$	−8.36737	+	4.83090i	−1.14935	+	0.663576i	−0.948728	−	0.316094i	$-0.897629\pi$
$53$	−8.36737	+	4.83090i	−1.14935	+	0.663576i	−0.200619	+	0.979669i	$0.564295\pi$
$54$		0			0
$55$			13.9140i			1.87616i
$56$		0			0
$57$	−4.63746	+	2.51371i	−0.614246	+	0.332949i
$58$		0			0
$59$	5.06580	+	8.77423i	0.659512	+	1.14231i	0.980742	+	0.195307i	$0.0625702\pi$
$59$	5.06580	+	8.77423i	0.659512	+	1.14231i	−0.321231	+	0.947001i	$0.604096\pi$
$60$		0			0
$61$	5.63746	−	9.76436i	0.721803	−	1.25020i	−0.238474	−	0.971149i	$-0.576647\pi$
$61$	5.63746	−	9.76436i	0.721803	−	1.25020i	0.960277	−	0.279050i	$-0.0900195\pi$
$62$		0			0
$63$	−4.84488	+	6.28706i	−0.610398	+	0.792095i
$64$		0			0
$65$	6.83004	+	3.94333i	0.847163	+	0.489110i
$66$		0			0
$67$	−13.9124	+	8.03231i	−1.69967	+	0.981303i	−0.753600	+	0.657333i	$0.771684\pi$
$67$	−13.9124	+	8.03231i	−1.69967	+	0.981303i	−0.946067	+	0.323970i	$0.894982\pi$
$68$		0			0
$69$	−1.36254	−	2.51371i	−0.164031	−	0.302615i
$70$		0			0
$71$	−10.3585			−1.22933			−0.614665	−	0.788788i	$-0.710709\pi$
$71$	−10.3585			−1.22933			−0.614665	+	0.788788i	$0.710709\pi$
$72$		0			0
$73$	3.63746	+	6.30026i	0.425732	+	0.737390i	0.996489	−	0.0837296i	$-0.0266832\pi$
$73$	3.63746	+	6.30026i	0.425732	+	0.737390i	−0.570756	+	0.821120i	$0.693350\pi$
$74$		0			0
$75$	18.2662	+	0.491189i	2.10920	+	0.0567176i
$76$		0			0
$77$	5.29272	−	7.69014i	0.603161	−	0.876373i
$78$		0			0
$79$	4.50000	+	2.59808i	0.506290	+	0.292306i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	4.50000	+	2.59808i	0.506290	+	0.292306i	−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	−5.31055	+	7.26622i	−0.590061	+	0.807358i
$82$		0			0
$83$	−5.17926			−0.568498			−0.284249	−	0.958751i	$-0.591744\pi$
$83$	−5.17926			−0.568498			−0.284249	+	0.958751i	$0.591744\pi$
$84$		0			0
$85$	−19.8248			−2.15030
$86$		0			0
$87$	−10.0418	−	6.16335i	−1.07659	−	0.660781i
$88$		0			0
$89$	−6.23157	−	3.59780i	−0.660545	−	0.381366i	0.131940	−	0.991258i	$-0.457879\pi$
$89$	−6.23157	−	3.59780i	−0.660545	−	0.381366i	−0.792485	+	0.609892i	$0.791213\pi$
$90$		0			0
$91$	−2.27492	−	4.77753i	−0.238476	−	0.500821i
$92$		0			0
$93$	0.0806424	−	2.99892i	0.00836223	−	0.310973i
$94$		0			0
$95$	−6.00465	−	10.4004i	−0.616064	−	1.06705i
$96$		0			0
$97$	4.27492			0.434052			0.217026	−	0.976166i	$-0.430364\pi$
$97$	4.27492			0.434052			0.217026	+	0.976166i	$0.430364\pi$
$98$		0			0
$99$	5.77774	−	8.86957i	0.580685	−	0.891425i
$100$		0			0
$101$	11.1839	−	6.45704i	1.11284	−	0.642499i	0.173277	−	0.984873i	$-0.444564\pi$
$101$	11.1839	−	6.45704i	1.11284	−	0.642499i	0.939564	+	0.342374i	$0.111231\pi$
$102$		0			0
$103$	4.18729	+	2.41753i	0.412586	+	0.238207i	0.691900	−	0.721993i	$-0.256774\pi$
$103$	4.18729	+	2.41753i	0.412586	+	0.238207i	−0.279314	+	0.960200i	$0.590107\pi$
$104$		0			0
$105$	−14.6050	−	10.6415i	−1.42530	−	1.03850i
$106$		0			0
$107$	0.113457	−	0.196514i	0.0109683	−	0.0189977i	−0.860489	−	0.509469i	$-0.829842\pi$
$107$	0.113457	−	0.196514i	0.0109683	−	0.0189977i	0.871457	+	0.490471i	$0.163175\pi$
$108$		0			0
$109$	3.91238	+	6.77643i	0.374738	+	0.649065i	0.990288	−	0.139033i	$-0.0443995\pi$
$109$	3.91238	+	6.77643i	0.374738	+	0.649065i	−0.615550	+	0.788098i	$0.711066\pi$
$110$		0			0
$111$	1.05231	+	1.94136i	0.0998804	+	0.184266i
$112$		0			0
$113$			2.16818i			0.203965i	0.994786	+	0.101982i	$0.0325186\pi$
$113$			2.16818i			0.203965i	−0.994786	+	0.101982i	$0.967481\pi$
$114$		0			0
$115$	5.63746	−	3.25479i	0.525696	−	0.303511i
$116$		0			0
$117$	−2.71641	−	5.34987i	−0.251132	−	0.494596i
$118$		0			0
$119$	10.9570	+	7.54112i	1.00443	+	0.691294i
$120$		0			0
$121$	−0.725083	+	1.25588i	−0.0659166	+	0.114171i
$122$		0			0
$123$	−3.20062	−	1.96444i	−0.288590	−	0.177128i
$124$		0			0
$125$			21.8848i			1.95744i
$126$		0			0
$127$			4.77753i			0.423937i	0.977277	+	0.211968i	$0.0679874\pi$
$127$			4.77753i			0.423937i	−0.977277	+	0.211968i	$0.932013\pi$
$128$		0			0
$129$	1.23594	+	0.758580i	0.108818	+	0.0667892i
$130$		0			0
$131$	−1.76424	+	3.05575i	−0.154142	+	0.266982i	−0.932746	−	0.360533i	$-0.882595\pi$
$131$	−1.76424	+	3.05575i	−0.154142	+	0.266982i	0.778604	+	0.627516i	$0.215928\pi$
$132$		0			0
$133$	−0.637459	+	8.03231i	−0.0552747	+	0.696490i
$134$		0			0
$135$	−16.8619	−	11.6414i	−1.45124	−	1.00193i
$136$		0			0
$137$	−0.598477	+	0.345531i	−0.0511313	+	0.0295207i	−0.525348	−	0.850888i	$-0.676065\pi$
$137$	−0.598477	+	0.345531i	−0.0511313	+	0.0295207i	0.474216	+	0.880408i	$0.342731\pi$
$138$		0			0
$139$		−	20.8997i		−	1.77269i	−0.463026	−	0.886345i	$-0.653236\pi$
$139$		−	20.8997i		−	1.77269i	0.463026	−	0.886345i	$-0.346764\pi$
$140$		0			0
$141$	4.08762	+	7.54112i	0.344240	+	0.635077i
$142$		0			0
$143$	3.52848	+	6.11151i	0.295066	+	0.511070i
$144$		0			0
$145$	13.4124	−	23.2309i	1.11384	−	1.92922i
$146$		0			0
$147$	4.02414	+	11.4371i	0.331906	+	0.943313i
$148$		0			0
$149$	−6.23157	−	3.59780i	−0.510510	−	0.294743i	0.222533	−	0.974925i	$-0.428567\pi$
$149$	−6.23157	−	3.59780i	−0.510510	−	0.294743i	−0.733043	+	0.680182i	$0.761901\pi$
$150$		0			0
$151$	−0.774917	+	0.447399i	−0.0630619	+	0.0364088i	−0.531199	−	0.847247i	$-0.678259\pi$
$151$	−0.774917	+	0.447399i	−0.0630619	+	0.0364088i	0.468138	+	0.883656i	$0.344925\pi$
$152$		0			0
$153$	12.6375	+	8.23219i	1.02168	+	0.665533i
$154$		0			0
$155$	6.83004			0.548602
$156$		0			0
$157$	−7.18729	−	12.4488i	−0.573608	−	0.993519i	−0.996191	−	0.0871947i	$-0.972210\pi$
$157$	−7.18729	−	12.4488i	−0.573608	−	0.993519i	0.422583	−	0.906324i	$-0.361124\pi$
$158$		0			0
$159$	−0.449843	+	16.7287i	−0.0356749	+	1.32667i
$160$		0			0
$161$	−4.35387	−	0.345531i	−0.343133	−	0.0272316i
$162$		0			0
$163$	5.63746	+	3.25479i	0.441560	+	0.254935i	0.704259	−	0.709943i	$-0.251279\pi$
$163$	5.63746	+	3.25479i	0.441560	+	0.254935i	−0.262699	+	0.964878i	$0.584613\pi$
$164$		0			0
$165$	20.5395	+	12.6065i	1.59900	+	0.981415i
$166$		0			0
$167$	14.1139			1.09217			0.546084	−	0.837731i	$-0.316118\pi$
$167$	14.1139			1.09217			0.546084	+	0.837731i	$0.316118\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	−0.491012	+	9.12322i	−0.0375486	+	0.697670i
$172$		0			0
$173$	7.42852	+	4.28886i	0.564780	+	0.326076i	0.755062	−	0.655654i	$-0.227607\pi$
$173$	7.42852	+	4.28886i	0.564780	+	0.326076i	−0.190282	+	0.981730i	$0.560940\pi$
$174$		0			0
$175$	15.8248	−	22.9928i	1.19624	−	1.73809i
$176$		0			0
$177$	17.5421	+	0.471717i	1.31855	+	0.0354564i
$178$		0			0
$179$	−4.12696	−	7.14810i	−0.308463	−	0.534274i	0.669563	−	0.742755i	$-0.266481\pi$
$179$	−4.12696	−	7.14810i	−0.308463	−	0.534274i	−0.978026	+	0.208481i	$0.933148\pi$
$180$		0			0
$181$	15.0997			1.12235			0.561175	−	0.827697i	$-0.310350\pi$
$181$	15.0997			1.12235			0.561175	+	0.827697i	$0.310350\pi$
$182$		0			0
$183$	−9.30622	−	17.1687i	−0.687935	−	1.26915i
$184$		0			0
$185$	−4.35387	+	2.51371i	−0.320103	+	0.184812i
$186$		0			0
$187$	−15.3625	−	8.86957i	−1.12342	−	0.648607i
$188$		0			0
$189$	4.89120	+	12.8482i	0.355782	+	0.934569i
$190$		0			0
$191$	9.30622	−	16.1188i	0.673374	−	1.16632i	−0.303567	−	0.952810i	$-0.598178\pi$
$191$	9.30622	−	16.1188i	0.673374	−	1.16632i	0.976941	−	0.213508i	$-0.0684891\pi$
$192$		0			0
$193$	−6.04983	−	10.4786i	−0.435477	−	0.754268i	0.561858	−	0.827234i	$-0.310087\pi$
$193$	−6.04983	−	10.4786i	−0.435477	−	0.754268i	−0.997334	+	0.0729662i	$0.976753\pi$
$194$		0			0
$195$	12.0093	−	6.50958i	0.860004	−	0.466160i
$196$		0			0
$197$		−	17.9415i		−	1.27828i	−0.769091	−	0.639139i	$-0.779291\pi$
$197$		−	17.9415i		−	1.27828i	0.769091	−	0.639139i	$-0.220709\pi$
$198$		0			0
$199$	18.3625	−	10.6016i	1.30169	−	0.751529i	0.320993	−	0.947082i	$-0.395983\pi$
$199$	18.3625	−	10.6016i	1.30169	−	0.751529i	0.980693	+	0.195553i	$0.0626501\pi$
$200$		0			0
$201$	−0.747952	+	27.8147i	−0.0527565	+	1.96190i
$202$		0			0
$203$	−16.2497	+	7.73764i	−1.14051	+	0.543076i
$204$		0			0
$205$	4.27492	−	7.40437i	0.298573	−	0.517144i
$206$		0			0
$207$	−4.94519	−	0.266150i	−0.343715	−	0.0184987i
$208$		0			0
$209$		−	10.7459i		−	0.743309i
$210$		0			0
$211$		−	1.78959i		−	0.123201i	−0.998101	−	0.0616004i	$-0.980380\pi$
$211$		−	1.78959i		−	0.123201i	0.998101	−	0.0616004i	$-0.0196204\pi$
$212$		0			0
$213$	−9.38517	+	15.2910i	−0.643061	+	1.04772i
$214$		0			0
$215$	−1.65078	+	2.85924i	−0.112582	+	0.194998i
$216$		0			0
$217$	−3.77492	−	2.59808i	−0.256258	−	0.176369i
$218$		0			0
$219$	12.5960	+	0.338712i	0.851157	+	0.0228881i
$220$		0			0
$221$	−8.70774	+	5.02742i	−0.585746	+	0.338181i
$222$		0			0
$223$			10.0312i			0.671740i	0.941908	+	0.335870i	$0.109030\pi$
$223$			10.0312i			0.671740i	−0.941908	+	0.335870i	$0.890970\pi$
$224$		0			0
$225$	17.2749	−	26.5192i	1.15166	−	1.76795i
$226$		0			0
$227$	−13.7735	−	23.8565i	−0.914182	−	1.58341i	−0.808094	−	0.589054i	$-0.799501\pi$
$227$	−13.7735	−	23.8565i	−0.914182	−	1.58341i	−0.106088	−	0.994357i	$-0.533833\pi$
$228$		0			0
$229$	−4.36254	+	7.55614i	−0.288285	+	0.499324i	−0.973400	−	0.229110i	$-0.926418\pi$
$229$	−4.36254	+	7.55614i	−0.288285	+	0.499324i	0.685116	+	0.728434i	$0.259752\pi$
$230$		0			0
$231$	−6.55664	−	14.7805i	−0.431395	−	0.972487i
$232$		0			0
$233$	−0.598477	−	0.345531i	−0.0392075	−	0.0226365i	0.480268	−	0.877122i	$-0.340539\pi$
$233$	−0.598477	−	0.345531i	−0.0392075	−	0.0226365i	−0.519476	+	0.854485i	$0.673873\pi$
$234$		0			0
$235$	−16.9124	+	9.76436i	−1.10324	+	0.636957i
$236$		0			0
$237$	7.91238	−	4.28886i	0.513964	−	0.278591i
$238$		0			0
$239$	16.9617			1.09716			0.548579	−	0.836099i	$-0.315169\pi$
$239$	16.9617			1.09716			0.548579	+	0.836099i	$0.315169\pi$
$240$		0			0
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	0.731001	−	0.682376i	$-0.239053\pi$
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	−0.956456	+	0.291877i	$0.905720\pi$
$242$		0			0
$243$	5.91470	+	14.4228i	0.379428	+	0.925221i
$244$		0			0
$245$	−25.7829	+	9.85832i	−1.64721	+	0.629825i
$246$		0			0
$247$	−5.27492	−	3.04547i	−0.335635	−	0.193779i
$248$		0			0
$249$	−4.69259	+	7.64551i	−0.297381	+	0.484515i
$250$		0			0
$251$	11.7824			0.743698			0.371849	−	0.928293i	$-0.378724\pi$
$251$	11.7824			0.743698			0.371849	+	0.928293i	$0.378724\pi$
$252$		0			0
$253$	5.82475			0.366199
$254$		0			0
$255$	−17.9619	+	29.2649i	−1.12482	+	1.83264i
$256$		0			0
$257$	14.9393	+	8.62521i	0.931888	+	0.538026i	0.887408	−	0.460984i	$-0.152504\pi$
$257$	14.9393	+	8.62521i	0.931888	+	0.538026i	0.0444801	+	0.999010i	$0.485837\pi$
$258$		0			0
$259$	3.36254	+	0.266857i	0.208938	+	0.0165817i
$260$		0			0
$261$	−18.1964	+	9.23929i	−1.12633	+	0.571897i
$262$		0			0
$263$	10.9570	+	18.9781i	0.675638	+	1.17024i	0.976282	+	0.216502i	$0.0694649\pi$
$263$	10.9570	+	18.9781i	0.675638	+	1.17024i	−0.300645	+	0.953736i	$0.597202\pi$
$264$		0			0
$265$	−38.0997			−2.34044
$266$		0			0
$267$	−10.9570	+	5.93918i	−0.670558	+	0.363472i
$268$		0			0
$269$	3.41502	−	1.97166i	0.208218	−	0.120214i	−0.392265	−	0.919852i	$-0.628308\pi$
$269$	3.41502	−	1.97166i	0.208218	−	0.120214i	0.600483	+	0.799638i	$0.294975\pi$
$270$		0			0
$271$	−2.95017	−	1.70328i	−0.179210	−	0.103467i	0.407712	−	0.913111i	$-0.366327\pi$
$271$	−2.95017	−	1.70328i	−0.179210	−	0.103467i	−0.586921	+	0.809644i	$0.699660\pi$
$272$		0			0
$273$	−9.11363	−	0.970415i	−0.551582	−	0.0587322i
$274$		0			0
$275$	−18.6124	+	32.2377i	−1.12237	+	1.94401i
$276$		0			0
$277$	−6.63746	−	11.4964i	−0.398806	−	0.690753i	0.594773	−	0.803894i	$-0.297242\pi$
$277$	−6.63746	−	11.4964i	−0.398806	−	0.690753i	−0.993579	+	0.113141i	$0.963909\pi$
$278$		0			0
$279$	−4.35387	−	2.83616i	−0.260659	−	0.169797i
$280$		0			0
$281$			15.7733i			0.940957i	0.882411	+	0.470478i	$0.155919\pi$
$281$			15.7733i			0.940957i	−0.882411	+	0.470478i	$0.844081\pi$
$282$		0			0
$283$	17.7371	−	10.2405i	1.05436	−	0.608737i	0.130495	−	0.991449i	$-0.458343\pi$
$283$	17.7371	−	10.2405i	1.05436	−	0.608737i	0.923868	+	0.382712i	$0.125010\pi$
$284$		0			0
$285$	−20.7932	−	0.559141i	−1.23168	−	0.0331206i
$286$		0			0
$287$	−5.17926	+	2.46621i	−0.305722	+	0.145576i
$288$		0			0
$289$	4.13746	−	7.16629i	0.243380	−	0.421546i
$290$		0			0
$291$	3.87322	−	6.31054i	0.227052	−	0.369930i
$292$		0			0
$293$		−	13.3071i		−	0.777409i	−0.921362	−	0.388705i	$-0.872923\pi$
$293$		−	13.3071i		−	0.777409i	0.921362	−	0.388705i	$-0.127077\pi$
$294$		0			0
$295$			39.9523i			2.32611i
$296$		0			0
$297$	−7.85824	−	16.5651i	−0.455981	−	0.961205i
$298$		0			0
$299$	1.65078	−	2.85924i	0.0954672	−	0.165354i
$300$		0			0
$301$	2.00000	−	0.952341i	0.115278	−	0.0548920i
$302$		0			0
$303$	0.601265	−	22.3597i	0.0345418	−	1.28453i
$304$		0			0
$305$	38.5041	−	22.2303i	2.20474	−	1.27291i
$306$		0			0
$307$			17.3205i			0.988534i	0.869310	+	0.494267i	$0.164563\pi$
$307$			17.3205i			0.988534i	−0.869310	+	0.494267i	$0.835437\pi$
$308$		0			0
$309$	7.36254	−	3.99082i	0.418840	−	0.227030i
$310$		0			0
$311$	−11.1839	−	19.3711i	−0.634182	−	1.09843i	−0.986688	−	0.162625i	$-0.948004\pi$
$311$	−11.1839	−	19.3711i	−0.634182	−	1.09843i	0.352506	−	0.935809i	$-0.385330\pi$
$312$		0			0
$313$	2.22508	−	3.85396i	0.125769	−	0.217838i	−0.796264	−	0.604949i	$-0.793193\pi$
$313$	2.22508	−	3.85396i	0.125769	−	0.217838i	0.922033	+	0.387111i	$0.126527\pi$
$314$		0			0
$315$	−28.9413	+	11.9180i	−1.63066	+	0.671501i
$316$		0			0
$317$	5.29272	+	3.05575i	0.297269	+	0.171628i	0.641215	−	0.767361i	$-0.278431\pi$
$317$	5.29272	+	3.05575i	0.297269	+	0.171628i	−0.343947	+	0.938989i	$0.611764\pi$
$318$		0			0
$319$	20.7870	−	12.0014i	1.16385	−	0.671947i
$320$		0			0
$321$	−0.187293	−	0.345531i	−0.0104537	−	0.0192857i
$322$		0			0
$323$	15.3109			0.851920
$324$		0			0
$325$	10.5498	+	18.2728i	0.585200	+	1.01360i
$326$		0			0
$327$	13.5480	+	0.364312i	0.749204	+	0.0201465i
$328$		0			0
$329$	13.0616	+	1.03659i	0.720110	+	0.0571492i
$330$		0			0
$331$	24.4622	+	14.1233i	1.34456	+	0.776285i	0.987474	−	0.157785i	$-0.0504352\pi$
$331$	24.4622	+	14.1233i	1.34456	+	0.776285i	0.357091	+	0.934070i	$0.383769\pi$
$332$		0			0
$333$	3.81922	+	0.205551i	0.209292	+	0.0112641i
$334$		0			0
$335$	−63.3481			−3.46108
$336$		0			0
$337$	−20.8248			−1.13440			−0.567198	−	0.823581i	$-0.691973\pi$
$337$	−20.8248			−1.13440			−0.567198	+	0.823581i	$0.691973\pi$
$338$		0			0
$339$	3.20062	+	1.96444i	0.173834	+	0.106694i
$340$		0			0
$341$	5.29272	+	3.05575i	0.286617	+	0.165478i
$342$		0			0
$343$	18.0000	+	4.35890i	0.971909	+	0.235358i
$344$		0			0
$345$	0.303079	−	11.2708i	0.0163172	−	0.606802i
$346$		0			0
$347$	−11.1839	−	19.3711i	−0.600384	−	1.03990i	−0.992763	−	0.120092i	$-0.961681\pi$
$347$	−11.1839	−	19.3711i	−0.600384	−	1.03990i	0.392379	−	0.919804i	$-0.371652\pi$
$348$		0			0
$349$	5.45017			0.291741			0.145870	−	0.989304i	$-0.453402\pi$
$349$	5.45017			0.291741			0.145870	+	0.989304i	$0.453402\pi$
$350$		0			0
$351$	−10.3585	−	0.837253i	−0.552897	−	0.0446893i
$352$		0			0
$353$	−4.35387	+	2.51371i	−0.231733	+	0.133791i	−0.611371	−	0.791344i	$-0.709382\pi$
$353$	−4.35387	+	2.51371i	−0.231733	+	0.133791i	0.379638	+	0.925135i	$0.376048\pi$
$354$		0			0
$355$	−35.3746	−	20.4235i	−1.87749	−	1.08397i
$356$		0			0
$357$	21.0595	−	9.34198i	1.11458	−	0.494430i
$358$		0			0
$359$	−11.4108	+	19.7641i	−0.602241	+	1.04311i	0.390241	+	0.920713i	$0.372392\pi$
$359$	−11.4108	+	19.7641i	−0.602241	+	1.04311i	−0.992481	+	0.122398i	$0.960941\pi$
$360$		0			0
$361$	−4.86254	−	8.42217i	−0.255923	−	0.443272i
$362$		0			0
$363$	1.19695	+	2.20822i	0.0628238	+	0.115902i
$364$		0			0
$365$			28.6874i			1.50157i
$366$		0			0
$367$	−25.5997	+	14.7800i	−1.33629	+	0.771508i	−0.986255	−	0.165228i	$-0.947164\pi$
$367$	−25.5997	+	14.7800i	−1.33629	+	0.771508i	−0.350036	+	0.936736i	$0.613831\pi$
$368$		0			0
$369$	−5.79973	+	2.94483i	−0.301922	+	0.153302i
$370$		0			0
$371$	21.0574	+	14.4927i	1.09325	+	0.752424i
$372$		0			0
$373$	−14.9124	+	25.8290i	−0.772134	+	1.33737i	0.164258	+	0.986417i	$0.447477\pi$
$373$	−14.9124	+	25.8290i	−0.772134	+	1.33737i	−0.936392	+	0.350957i	$0.885856\pi$
$374$		0			0
$375$	32.3059	+	19.8284i	1.66827	+	1.02393i
$376$		0			0
$377$		−	13.6051i		−	0.700700i
$378$		0			0
$379$			10.3923i			0.533817i	0.963722	+	0.266908i	$0.0860021\pi$
$379$			10.3923i			0.533817i	−0.963722	+	0.266908i	$0.913998\pi$
$380$		0			0
$381$	7.05248	+	4.32860i	0.361310	+	0.221761i
$382$		0			0
$383$	14.4855	−	25.0896i	0.740173	−	1.28202i	−0.212243	−	0.977217i	$-0.568077\pi$
$383$	14.4855	−	25.0896i	0.740173	−	1.28202i	0.952416	−	0.304801i	$-0.0985900\pi$
$384$		0			0
$385$	33.2371	−	15.8265i	1.69392	−	0.806595i
$386$		0			0
$387$	2.23960	−	1.13716i	0.113845	−	0.0578052i
$388$		0			0
$389$	−19.8917	+	11.4845i	−1.00855	+	0.582285i	−0.910766	−	0.412923i	$-0.864508\pi$
$389$	−19.8917	+	11.4845i	−1.00855	+	0.582285i	−0.0977811	+	0.995208i	$0.531174\pi$
$390$		0			0
$391$			8.29917i			0.419707i
$392$		0			0
$393$	2.91238	+	5.37295i	0.146910	+	0.271029i
$394$		0			0
$395$	10.2451	+	17.7450i	0.515485	+	0.892847i
$396$		0			0
$397$	−3.18729	+	5.52055i	−0.159966	+	0.277069i	−0.934856	−	0.355027i	$-0.884472\pi$
$397$	−3.18729	+	5.52055i	−0.159966	+	0.277069i	0.774890	+	0.632096i	$0.217805\pi$
$398$		0			0
$399$	11.2796	+	8.21855i	0.564685	+	0.411442i
$400$		0			0
$401$	−31.6740	−	18.2870i	−1.58173	−	0.913210i	−0.994608	−	0.103709i	$-0.966929\pi$
$401$	−31.6740	−	18.2870i	−1.58173	−	0.913210i	−0.587119	−	0.809501i	$-0.699738\pi$
$402$		0			0
$403$	3.00000	−	1.73205i	0.149441	−	0.0862796i
$404$		0			0
$405$	−32.4622	+	14.3437i	−1.61306	+	0.712744i
$406$		0			0
$407$	−4.49852			−0.222983
$408$		0			0
$409$	8.22508	+	14.2463i	0.406704	+	0.704432i	0.994518	−	0.104564i	$-0.0333446\pi$
$409$	8.22508	+	14.2463i	0.406704	+	0.704432i	−0.587814	+	0.808996i	$0.700011\pi$
$410$		0			0
$411$	−0.0321751	+	1.19652i	−0.00158708	+	0.0590200i
$412$		0			0
$413$	15.1974	−	22.0813i	0.747816	−	1.08655i
$414$		0			0
$415$	−17.6873	−	10.2118i	−0.868235	−	0.501276i
$416$		0			0
$417$	−30.8517	−	18.9358i	−1.51081	−	0.927292i
$418$		0			0
$419$	30.1679			1.47380			0.736899	−	0.676002i	$-0.236289\pi$
$419$	30.1679			1.47380			0.736899	+	0.676002i	$0.236289\pi$
$420$		0			0
$421$	11.0997			0.540965			0.270482	−	0.962725i	$-0.412817\pi$
$421$	11.0997			0.540965			0.270482	+	0.962725i	$0.412817\pi$
$422$		0			0
$423$	14.8356	+	0.798450i	0.721330	+	0.0388220i
$424$		0			0
$425$	−45.9326	−	26.5192i	−2.22806	−	1.28637i
$426$		0			0
$427$	−29.7371	−	2.35999i	−1.43908	−	0.114208i
$428$		0			0
$429$	12.2186	+	0.328564i	0.589919	+	0.0158632i
$430$		0			0
$431$	12.8347	+	22.2303i	0.618226	+	1.07080i	0.989809	+	0.142399i	$0.0454815\pi$
$431$	12.8347	+	22.2303i	0.618226	+	1.07080i	−0.371584	+	0.928399i	$0.621185\pi$
$432$		0			0
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$	−22.1409	−	40.8471i	−1.06158	−	1.95847i
$436$		0			0
$437$	−4.35387	+	2.51371i	−0.208274	+	0.120247i
$438$		0			0
$439$	−8.32475	−	4.80630i	−0.397319	−	0.229392i	0.288008	−	0.957628i	$-0.407007\pi$
$439$	−8.32475	−	4.80630i	−0.397319	−	0.229392i	−0.685326	+	0.728236i	$0.740340\pi$
$440$		0			0
$441$	20.5291	+	4.42200i	0.977578	+	0.210572i
$442$		0			0
$443$	17.0751	−	29.5750i	0.811263	−	1.40515i	−0.100717	−	0.994915i	$-0.532114\pi$
$443$	17.0751	−	29.5750i	0.811263	−	1.40515i	0.911980	−	0.410234i	$-0.134553\pi$
$444$		0			0
$445$	−14.1873	−	24.5731i	−0.672542	−	1.16488i
$446$		0			0
$447$	−10.9570	+	5.93918i	−0.518248	+	0.280914i
$448$		0			0
$449$			29.3784i			1.38645i	0.720719	+	0.693227i	$0.243812\pi$
$449$			29.3784i			1.38645i	−0.720719	+	0.693227i	$0.756188\pi$
$450$		0			0
$451$	6.62541	−	3.82518i	0.311979	−	0.180121i
$452$		0			0
$453$	−0.0416608	+	1.54927i	−0.00195740	+	0.0727913i
$454$		0			0
$455$	1.65078	−	20.8007i	0.0773899	−	0.975153i
$456$		0			0
$457$	−14.3248	+	24.8112i	−0.670084	+	1.16062i	0.307796	+	0.951452i	$0.400408\pi$
$457$	−14.3248	+	24.8112i	−0.670084	+	1.16062i	−0.977880	+	0.209167i	$0.932925\pi$
$458$		0			0
$459$	23.6021	−	11.1965i	1.10165	−	0.522608i
$460$		0			0
$461$		−	13.6051i		−	0.633654i	−0.948483	−	0.316827i	$-0.897382\pi$
$461$		−	13.6051i		−	0.633654i	0.948483	−	0.316827i	$-0.102618\pi$
$462$		0			0
$463$		−	13.9715i		−	0.649310i	−0.945832	−	0.324655i	$-0.894752\pi$
$463$		−	13.9715i		−	0.649310i	0.945832	−	0.324655i	$-0.105248\pi$
$464$		0			0
$465$	6.18825	−	10.0824i	0.286973	−	0.467558i
$466$		0			0
$467$	14.4855	−	25.0896i	0.670308	−	1.16101i	−0.307509	−	0.951545i	$-0.599495\pi$
$467$	14.4855	−	25.0896i	0.670308	−	1.16101i	0.977817	−	0.209462i	$-0.0671714\pi$
$468$		0			0
$469$	35.0120	+	24.0969i	1.61671	+	1.11269i
$470$		0			0
$471$	−24.8885	−	0.669265i	−1.14680	−	0.0308381i
$472$		0			0
$473$	−2.55844	+	1.47712i	−0.117637	+	0.0679179i
$474$		0			0
$475$		−	32.1293i		−	1.47419i
$476$		0			0
$477$	24.2870	+	15.8208i	1.11202	+	0.724385i
$478$		0			0
$479$	−2.24926	−	3.89583i	−0.102771	−	0.178005i	0.810054	−	0.586355i	$-0.199438\pi$
$479$	−2.24926	−	3.89583i	−0.102771	−	0.178005i	−0.912825	+	0.408350i	$0.866104\pi$
$480$		0			0
$481$	−1.27492	+	2.20822i	−0.0581312	+	0.100686i
$482$		0			0
$483$	−4.45482	+	6.11403i	−0.202701	+	0.278198i
$484$		0			0
$485$	14.5989	+	8.42870i	0.662904	+	0.382728i
$486$		0			0
$487$	−2.22508	+	1.28465i	−0.100828	+	0.0582131i	−0.549566	−	0.835450i	$-0.685207\pi$
$487$	−2.22508	+	1.28465i	−0.100828	+	0.0582131i	0.448738	+	0.893663i	$0.351874\pi$
$488$		0			0
$489$	9.91238	−	5.37295i	0.448253	−	0.242973i
$490$		0			0
$491$	−22.1409			−0.999206			−0.499603	−	0.866255i	$-0.666521\pi$
$491$	−22.1409			−0.999206			−0.499603	+	0.866255i	$0.666521\pi$
$492$		0			0
$493$	17.0997	+	29.6175i	0.770130	+	1.33390i
$494$		0			0
$495$	37.2189	−	18.8980i	1.67287	−	0.849402i
$496$		0			0
$497$	11.7824	+	24.7441i	0.528512	+	1.10992i
$498$		0			0
$499$	22.1873	+	12.8098i	0.993240	+	0.573447i	0.906241	−	0.422761i	$-0.138939\pi$
$499$	22.1873	+	12.8098i	0.993240	+	0.573447i	0.0869986	+	0.996208i	$0.472272\pi$
$500$		0			0
$501$	12.7877	−	20.8347i	0.571312	−	0.930824i
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	50.9244			2.26611
$506$		0			0
$507$	−8.15430	+	13.2856i	−0.362145	+	0.590034i
$508$		0			0
$509$	−8.36737	−	4.83090i	−0.370877	−	0.214126i	0.302964	−	0.953002i	$-0.402024\pi$
$509$	−8.36737	−	4.83090i	−0.370877	−	0.214126i	−0.673842	+	0.738876i	$0.735357\pi$
$510$		0			0
$511$	10.9124	−	15.8553i	0.482735	−	0.701398i
$512$		0			0
$513$	13.0226	+	8.99077i	0.574963	+	0.396952i
$514$		0			0
$515$	9.53313	+	16.5119i	0.420080	+	0.727600i
$516$		0			0
$517$	−17.4743			−0.768517
$518$		0			0
$519$	13.0616	−	7.07997i	0.573341	−	0.310776i
$520$		0			0
$521$	16.8170	−	9.70930i	0.736766	−	0.425372i	−0.0841261	−	0.996455i	$-0.526810\pi$
$521$	16.8170	−	9.70930i	0.736766	−	0.425372i	0.820892	+	0.571083i	$0.193477\pi$
$522$		0			0
$523$	−21.4622	−	12.3912i	−0.938477	−	0.541830i	−0.0489944	−	0.998799i	$-0.515602\pi$
$523$	−21.4622	−	12.3912i	−0.938477	−	0.541830i	−0.889483	+	0.456969i	$0.848935\pi$
$524$		0			0
$525$	−19.6038	−	44.1924i	−0.855578	−	1.92872i
$526$		0			0
$527$	−4.35387	+	7.54112i	−0.189658	+	0.328497i
$528$		0			0
$529$	10.1375	+	17.5586i	0.440759	+	0.763417i
$530$		0			0
$531$	16.5901	−	25.4679i	0.719949	−	1.10521i
$532$		0			0
$533$		−	4.33635i		−	0.187828i
$534$		0			0
$535$	0.774917	−	0.447399i	0.0335026	−	0.0193427i
$536$		0			0
$537$	−14.2910	−	0.384293i	−0.616703	−	0.0165835i
$538$		0			0
$539$	−24.3902	−	3.89583i	−1.05056	−	0.167805i
$540$		0			0
$541$	13.3625	−	23.1446i	0.574501	−	0.995064i	−0.421595	−	0.906784i	$-0.638530\pi$
$541$	13.3625	−	23.1446i	0.574501	−	0.995064i	0.996096	−	0.0882799i	$-0.0281370\pi$
$542$		0			0
$543$	13.6808	−	22.2898i	0.587100	−	0.956547i
$544$		0			0
$545$			30.8556i			1.32171i
$546$		0			0
$547$			13.0192i			0.556659i	0.960486	+	0.278329i	$0.0897807\pi$
$547$			13.0192i			0.556659i	−0.960486	+	0.278329i	$0.910219\pi$
$548$		0			0
$549$	−33.7759	−	1.81782i	−1.44152	−	0.0775825i
$550$		0			0
$551$	−10.3585	+	17.9415i	−0.441288	+	0.764333i
$552$		0			0
$553$	1.08762	−	13.7046i	0.0462505	−	0.582780i
$554$		0			0
$555$	−0.234071	+	8.70459i	−0.00993577	+	0.369489i
$556$		0			0
$557$	13.3197	−	7.69014i	0.564375	−	0.325842i	−0.190525	−	0.981682i	$-0.561019\pi$
$557$	13.3197	−	7.69014i	0.564375	−	0.325842i	0.754899	+	0.655841i	$0.227686\pi$
$558$		0			0
$559$			1.67451i			0.0708241i
$560$		0			0
$561$	−27.0120	+	14.6417i	−1.14045	+	0.618174i
$562$		0			0
$563$	14.0005	+	24.2495i	0.590049	+	1.02199i	0.994225	+	0.107314i	$0.0342249\pi$
$563$	14.0005	+	24.2495i	0.590049	+	1.02199i	−0.404176	+	0.914681i	$0.632442\pi$
$564$		0			0
$565$	−4.27492	+	7.40437i	−0.179847	+	0.311504i
$566$		0			0
$567$	23.3978	+	4.42062i	0.982616	+	0.185649i
$568$		0			0
$569$	32.8710	+	18.9781i	1.37802	+	0.795603i	0.991921	−	0.126853i	$-0.0404877\pi$
$569$	32.8710	+	18.9781i	1.37802	+	0.795603i	0.386103	+	0.922456i	$0.373821\pi$
$570$		0			0
$571$	15.4622	−	8.92711i	0.647073	−	0.373588i	−0.140261	−	0.990115i	$-0.544794\pi$
$571$	15.4622	−	8.92711i	0.647073	−	0.373588i	0.787334	+	0.616527i	$0.211461\pi$
$572$		0			0
$573$	−15.3625	−	28.3419i	−0.641779	−	1.18400i
$574$		0			0
$575$	17.4155			0.726276
$576$		0			0
$577$	17.0498	+	29.5312i	0.709794	+	1.22940i	0.964933	+	0.262495i	$0.0845453\pi$
$577$	17.0498	+	29.5312i	0.709794	+	1.22940i	−0.255140	+	0.966904i	$0.582121\pi$
$578$		0			0
$579$	−20.9497	−	0.563348i	−0.870639	−	0.0234119i
$580$		0			0
$581$	5.89120	+	12.3720i	0.244408	+	0.513278i
$582$		0			0
$583$	−29.5241	−	17.0457i	−1.22276	−	0.705962i
$584$		0			0
$585$	1.27154	−	23.6258i	0.0525717	−	0.976806i
$586$		0			0
$587$	5.17926			0.213771			0.106886	−	0.994271i	$-0.465912\pi$
$587$	5.17926			0.213771			0.106886	+	0.994271i	$0.465912\pi$
$588$		0			0
$589$	−5.27492			−0.217349
$590$		0			0
$591$	−26.4848	−	16.2556i	−1.08944	−	0.668666i
$592$		0			0
$593$	11.1839	+	6.45704i	0.459268	+	0.265159i	0.711737	−	0.702446i	$-0.247909\pi$
$593$	11.1839	+	6.45704i	0.459268	+	0.265159i	−0.252468	+	0.967605i	$0.581242\pi$
$594$		0			0
$595$	22.5498	+	47.3566i	0.924453	+	1.94143i
$596$		0			0
$597$	0.987200	−	36.7118i	0.0404034	−	1.50251i
$598$		0			0
$599$	0.598477	+	1.03659i	0.0244531	+	0.0423540i	0.877993	−	0.478673i	$-0.158882\pi$
$599$	0.598477	+	1.03659i	0.0244531	+	0.0423540i	−0.853540	+	0.521028i	$0.825549\pi$
$600$		0			0
$601$	17.9244			0.731152			0.365576	−	0.930781i	$-0.380872\pi$
$601$	17.9244			0.731152			0.365576	+	0.930781i	$0.380872\pi$
$602$		0			0
$603$	40.3818	+	26.3052i	1.64447	+	1.07123i
$604$		0			0
$605$	−4.95235	+	2.85924i	−0.201342	+	0.116245i
$606$		0			0
$607$	−30.0498	−	17.3493i	−1.21969	−	0.704186i	−0.254835	−	0.966985i	$-0.582021\pi$
$607$	−30.0498	−	17.3493i	−1.21969	−	0.704186i	−0.964851	+	0.262799i	$0.915354\pi$
$608$		0			0
$609$	−3.30066	+	30.9980i	−0.133749	+	1.25610i
$610$		0			0
$611$	−4.95235	+	8.57772i	−0.200351	+	0.347017i
$612$		0			0
$613$	−18.9124	−	32.7572i	−0.763864	−	1.32305i	−0.940845	−	0.338837i	$-0.889967\pi$
$613$	−18.9124	−	32.7572i	−0.763864	−	1.32305i	0.176982	−	0.984214i	$-0.443367\pi$
$614$		0			0
$615$	−7.05696	−	13.0192i	−0.284564	−	0.524983i
$616$		0			0
$617$		−	38.0512i		−	1.53188i	−0.642911	−	0.765941i	$-0.722273\pi$
$617$		−	38.0512i		−	1.53188i	0.642911	−	0.765941i	$-0.277727\pi$
$618$		0			0
$619$	9.46221	−	5.46301i	0.380318	−	0.219577i	−0.297638	−	0.954679i	$-0.596199\pi$
$619$	9.46221	−	5.46301i	0.380318	−	0.219577i	0.677957	+	0.735102i	$0.262866\pi$
$620$		0			0
$621$	−4.87339	+	7.05884i	−0.195563	+	0.283262i
$622$		0			0
$623$	−1.50613	+	18.9781i	−0.0603420	+	0.760341i
$624$		0			0
$625$	−16.7749	+	29.0550i	−0.670997	+	1.16220i
$626$		0			0
$627$	−15.8629	−	9.73614i	−0.633502	−	0.388824i
$628$		0			0
$629$		−	6.40954i		−	0.255565i
$630$		0			0
$631$			37.0219i			1.47382i	0.675992	+	0.736909i	$0.263715\pi$
$631$			37.0219i			1.47382i	−0.675992	+	0.736909i	$0.736285\pi$
$632$		0			0
$633$	−2.64176	−	1.62143i	−0.105001	−	0.0644462i
$634$		0			0
$635$	−9.41968	+	16.3154i	−0.373808	+	0.647455i
$636$		0			0
$637$	−8.82475	+	10.8685i	−0.349649	+	0.430625i
$638$		0			0
$639$	14.0690	+	27.7084i	0.556561	+	1.09613i
$640$		0			0
$641$	−6.23157	+	3.59780i	−0.246132	+	0.142104i	−0.617992	−	0.786184i	$-0.712054\pi$
$641$	−6.23157	+	3.59780i	−0.246132	+	0.142104i	0.371860	+	0.928289i	$0.378720\pi$
$642$		0			0
$643$			6.09095i			0.240204i	0.992762	+	0.120102i	$0.0383221\pi$
$643$			6.09095i			0.240204i	−0.992762	+	0.120102i	$0.961678\pi$
$644$		0			0
$645$	2.72508	+	5.02742i	0.107300	+	0.197954i
$646$		0			0
$647$	−4.58078	−	7.93415i	−0.180089	−	0.311924i	0.761822	−	0.647787i	$-0.224305\pi$
$647$	−4.58078	−	7.93415i	−0.180089	−	0.311924i	−0.941911	+	0.335863i	$0.890972\pi$
$648$		0			0
$649$	−17.8746	+	30.9597i	−0.701639	+	1.21527i
$650$		0			0
$651$	−7.25543	+	3.21851i	−0.284363	+	0.126143i
$652$		0			0
$653$	−18.2721	−	10.5494i	−0.715041	−	0.412829i	0.0978837	−	0.995198i	$-0.468793\pi$
$653$	−18.2721	−	10.5494i	−0.715041	−	0.412829i	−0.812925	+	0.582369i	$0.802126\pi$
$654$		0			0
$655$	−12.0498	+	6.95698i	−0.470826	+	0.271832i
$656$		0			0
$657$	11.9124	−	18.2870i	0.464746	−	0.713445i
$658$		0			0
$659$	−45.1895			−1.76033			−0.880166	−	0.474666i	$-0.842569\pi$
$659$	−45.1895			−1.76033			−0.880166	+	0.474666i	$0.842569\pi$
$660$		0			0
$661$	−14.6375	−	25.3528i	−0.569331	−	0.986110i	−0.996632	−	0.0820011i	$-0.973869\pi$
$661$	−14.6375	−	25.3528i	−0.569331	−	0.986110i	0.427301	−	0.904109i	$-0.359464\pi$
$662$		0			0
$663$	−0.468142	+	17.4092i	−0.0181811	+	0.676117i
$664$		0			0
$665$	−18.0140	+	26.1737i	−0.698551	+	1.01497i
$666$		0			0
$667$	−9.72508	−	5.61478i	−0.376557	−	0.217405i
$668$		0			0
$669$	14.8079	+	9.08862i	0.572505	+	0.351387i
$670$		0			0
$671$	39.7833			1.53582
$672$		0			0
$673$	12.2749			0.473163			0.236582	−	0.971612i	$-0.423973\pi$
$673$	12.2749			0.473163			0.236582	+	0.971612i	$0.423973\pi$
$674$		0			0
$675$	−23.4954	−	49.5282i	−0.904339	−	1.90634i
$676$		0			0
$677$	10.9258	+	6.30802i	0.419913	+	0.242437i	0.695040	−	0.718971i	$-0.255387\pi$
$677$	10.9258	+	6.30802i	0.419913	+	0.242437i	−0.275127	+	0.961408i	$0.588720\pi$
$678$		0			0
$679$	−4.86254	−	10.2118i	−0.186607	−	0.391892i
$680$		0			0
$681$	−47.6957	−	1.28256i	−1.82770	−	0.0491479i
$682$		0			0
$683$	−12.3497	−	21.3903i	−0.472547	−	0.818476i	0.526959	−	0.849891i	$-0.323332\pi$
$683$	−12.3497	−	21.3903i	−0.472547	−	0.818476i	−0.999506	+	0.0314147i	$0.989999\pi$
$684$		0			0
$685$	−2.72508			−0.104120
$686$		0			0
$687$	7.20161	+	13.2860i	0.274758	+	0.506893i
$688$		0			0
$689$	−16.7347	+	9.66181i	−0.637543	+	0.368085i
$690$		0			0
$691$	26.7371	+	15.4367i	1.01713	+	0.587239i	0.913271	−	0.407353i	$-0.133548\pi$
$691$	26.7371	+	15.4367i	1.01713	+	0.587239i	0.103857	+	0.994592i	$0.466881\pi$
$692$		0			0
$693$	−27.7592	−	3.71288i	−1.05449	−	0.141041i
$694$		0			0
$695$	41.2072	−	71.3729i	1.56308	−	2.70733i
$696$		0			0
$697$	5.45017	+	9.43996i	0.206440	+	0.357564i
$698$		0			0
$699$	−1.05231	+	0.570396i	−0.0398018	+	0.0215744i
$700$		0			0
$701$		−	22.5759i		−	0.852679i	−0.904563	−	0.426340i	$-0.859803\pi$
$701$		−	22.5759i		−	0.852679i	0.904563	−	0.426340i	$-0.140197\pi$
$702$		0			0
$703$	3.36254	−	1.94136i	0.126821	−	0.0732199i
$704$		0			0
$705$	−0.909237	+	33.8125i	−0.0342438	+	1.27345i
$706$		0			0
$707$	−28.1456	−	19.3711i	−1.05852	−	0.728526i
$708$		0			0
$709$	10.1873	−	17.6449i	0.382592	−	0.662668i	−0.608840	−	0.793293i	$-0.708365\pi$
$709$	10.1873	−	17.6449i	0.382592	−	0.662668i	0.991432	+	0.130625i	$0.0416982\pi$
$710$		0			0
$711$	0.837758	−	15.5659i	0.0314184	−	0.583768i
$712$		0			0
$713$		−	2.85924i		−	0.107079i
$714$		0			0
$715$			27.8279i			1.04070i
$716$		0			0
$717$	15.3678	−	25.0384i	0.573922	−	0.935077i
$718$		0			0
$719$	−9.53313	+	16.5119i	−0.355526	+	0.615789i	−0.987208	−	0.159439i	$-0.949032\pi$
$719$	−9.53313	+	16.5119i	−0.355526	+	0.615789i	0.631682	+	0.775228i	$0.282365\pi$
$720$		0			0
$721$	1.01204	−	12.7523i	0.0376905	−	0.474920i
$722$		0			0
$723$	−12.1200	−	0.325913i	−0.450747	−	0.0121208i
$724$		0			0
$725$	62.1511	−	35.8830i	2.30824	−	1.33266i
$726$		0			0
$727$			10.7534i			0.398821i	0.979916	+	0.199411i	$0.0639027\pi$
$727$			10.7534i			0.398821i	−0.979916	+	0.199411i	$0.936097\pi$
$728$		0			0
$729$	26.6495	+	4.33635i	0.987019	+	0.160606i
$730$		0			0
$731$	−2.10461	−	3.64529i	−0.0778418	−	0.134826i
$732$		0			0
$733$	−16.6375	+	28.8169i	−0.614519	+	1.06438i	0.375950	+	0.926640i	$0.377316\pi$
$733$	−16.6375	+	28.8169i	−0.614519	+	1.06438i	−0.990469	+	0.137737i	$0.956017\pi$
$734$		0			0
$735$	−8.80749	+	46.9921i	−0.324869	+	1.73333i
$736$		0			0
$737$	−49.0895	−	28.3419i	−1.80824	−	1.04399i
$738$		0			0
$739$	−35.8368	+	20.6904i	−1.31828	+	0.761108i	−0.983451	−	0.181172i	$-0.942011\pi$
$739$	−35.8368	+	20.6904i	−1.31828	+	0.761108i	−0.334826	+	0.942280i	$0.608678\pi$
$740$		0			0
$741$	−9.27492	+	5.02742i	−0.340723	+	0.184687i
$742$		0			0
$743$	−33.9233			−1.24453			−0.622263	−	0.782808i	$-0.713786\pi$
$743$	−33.9233			−1.24453			−0.622263	+	0.782808i	$0.713786\pi$
$744$		0			0
$745$	−14.1873	−	24.5731i	−0.519782	−	0.900289i
$746$		0			0
$747$	7.03450	+	13.8542i	0.257379	+	0.506898i
$748$		0			0
$749$	−0.598477	−	0.0474962i	−0.0218679	−	0.00173547i
$750$		0			0
$751$	7.59967	+	4.38767i	0.277316	+	0.160108i	0.632208	−	0.774799i	$-0.282149\pi$
$751$	7.59967	+	4.38767i	0.277316	+	0.160108i	−0.354892	+	0.934907i	$0.615482\pi$
$752$		0			0
$753$	10.6752	−	17.3929i	0.389028	−	0.633833i
$754$		0			0
$755$	−3.52848			−0.128415
$756$		0			0
$757$	−15.0997			−0.548807			−0.274403	−	0.961615i	$-0.588480\pi$
$757$	−15.0997			−0.548807			−0.274403	+	0.961615i	$0.588480\pi$
$758$		0			0
$759$	5.27742	−	8.59837i	0.191558	−	0.312101i
$760$		0			0
$761$	3.67313	+	2.12068i	0.133151	+	0.0768746i	0.565096	−	0.825025i	$-0.308839\pi$
$761$	3.67313	+	2.12068i	0.133151	+	0.0768746i	−0.431945	+	0.901900i	$0.642173\pi$
$762$		0			0
$763$	11.7371	−	17.0537i	0.424913	−	0.617384i
$764$		0			0
$765$	26.9261	+	53.0299i	0.973515	+	1.91730i
$766$		0			0
$767$	10.1316	+	17.5485i	0.365831	+	0.633638i
$768$		0			0
$769$	−28.8248			−1.03945			−0.519724	−	0.854334i	$-0.673965\pi$
$769$	−28.8248			−1.03945			−0.519724	+	0.854334i	$0.673965\pi$
$770$		0			0
$771$	26.2679	−	14.2384i	0.946014	−	0.512782i
$772$		0			0
$773$	−47.2118	+	27.2578i	−1.69809	+	0.980394i	−0.750521	+	0.660846i	$0.770198\pi$
$773$	−47.2118	+	27.2578i	−1.69809	+	0.980394i	−0.947570	+	0.319547i	$0.896469\pi$
$774$		0			0
$775$	15.8248	+	9.13642i	0.568442	+	0.328190i
$776$		0			0
$777$	3.44050	−	4.72193i	0.123427	−	0.169398i
$778$		0			0
$779$	−3.30156	+	5.71848i	−0.118291	+	0.204886i
$780$		0			0
$781$	−18.2749	−	31.6531i	−0.653928	−	1.13264i
$782$		0			0
$783$	−2.84774	+	35.2323i	−0.101770	+	1.25910i
$784$		0			0
$785$		−	56.6837i		−	2.02313i
$786$		0			0
$787$	−32.7371	+	18.9008i	−1.16695	+	0.673740i	−0.952960	−	0.303095i	$-0.901980\pi$
$787$	−32.7371	+	18.9008i	−1.16695	+	0.673740i	−0.213992	+	0.976835i	$0.568647\pi$
$788$		0			0
$789$	37.9424	+	1.02029i	1.35079	+	0.0363234i
$790$		0			0
$791$	5.17926	−	2.46621i	0.184153	−	0.0876884i
$792$		0			0
$793$	11.2749	−	19.5287i	0.400384	−	0.693486i
$794$		0			0
$795$	−34.5196	+	56.2419i	−1.22428	+	1.99470i
$796$		0			0
$797$			24.7441i			0.876479i	0.898858	+	0.438240i	$0.144398\pi$
$797$			24.7441i			0.876479i	−0.898858	+	0.438240i	$0.855602\pi$
$798$		0			0
$799$		−	24.8975i		−	0.880811i
$800$		0			0
$801$	−1.16012	+	21.5556i	−0.0409909	+	0.761629i
$802$		0			0
$803$	−12.8347	+	22.2303i	−0.452927	+	0.784492i
$804$		0			0
$805$	−14.1873	−	9.76436i	−0.500036	−	0.344149i
$806$		0			0
$807$	0.183597	−	6.82758i	0.00646293	−	0.240342i
$808$		0			0
$809$	−41.5787	+	24.0055i	−1.46183	+	0.843988i	−0.999096	−	0.0425085i	$-0.986465\pi$
$809$	−41.5787	+	24.0055i	−1.46183	+	0.843988i	−0.462735	+	0.886497i	$0.653132\pi$
$810$		0			0
$811$		−	4.41644i		−	0.155082i	−0.996989	−	0.0775411i	$-0.975293\pi$
$811$		−	4.41644i		−	0.155082i	0.996989	−	0.0775411i	$-0.0247069\pi$
$812$		0			0
$813$	−5.18729	+	2.81174i	−0.181926	+	0.0986121i
$814$		0			0
$815$	12.8347	+	22.2303i	0.449580	+	0.778695i
$816$		0			0
$817$	1.27492	−	2.20822i	0.0446037	−	0.0772559i
$818$		0			0
$819$	−9.68976	+	12.5741i	−0.338588	+	0.439375i
$820$		0			0
$821$	34.4906	+	19.9132i	1.20373	+	0.694974i	0.961383	−	0.275216i	$-0.0887493\pi$
$821$	34.4906	+	19.9132i	1.20373	+	0.694974i	0.242347	+	0.970190i	$0.422083\pi$
$822$		0			0
$823$	16.9124	−	9.76436i	0.589528	−	0.340364i	−0.175383	−	0.984500i	$-0.556116\pi$
$823$	16.9124	−	9.76436i	0.589528	−	0.340364i	0.764911	+	0.644136i	$0.222783\pi$
$824$		0			0
$825$	30.7251	+	56.6837i	1.06971	+	1.97347i
$826$		0			0
$827$	−8.02700			−0.279126			−0.139563	−	0.990213i	$-0.544570\pi$
$827$	−8.02700			−0.279126			−0.139563	+	0.990213i	$0.544570\pi$
$828$		0			0
$829$	−5.18729	−	8.98466i	−0.180162	−	0.312050i	0.761774	−	0.647843i	$-0.224329\pi$
$829$	−5.18729	−	8.98466i	−0.180162	−	0.312050i	−0.941936	+	0.335793i	$0.890996\pi$
$830$		0			0
$831$	−22.9845	−	0.618066i	−0.797324	−	0.0214405i
$832$		0			0
$833$	5.55082	−	34.7514i	0.192325	−	1.20406i
$834$		0			0
$835$	48.1993	+	27.8279i	1.66801	+	0.963024i
$836$		0			0
$837$	−8.13143	+	3.85743i	−0.281063	+	0.133332i
$838$		0			0
$839$	20.7170			0.715232			0.357616	−	0.933869i	$-0.383590\pi$
$839$	20.7170			0.715232			0.357616	+	0.933869i	$0.383590\pi$
$840$		0			0
$841$	−17.2749			−0.595687
$842$		0			0
$843$	23.2842	+	14.2912i	0.801951	+	0.492213i
$844$		0			0
$845$	−30.7352	−	17.7450i	−1.05732	−	0.610446i
$846$		0			0
$847$	3.82475	+	0.303539i	0.131420	+	0.0104297i
$848$		0			0
$849$	0.953577	−	35.4614i	0.0327267	−	1.21703i
$850$		0			0
$851$	1.05231	+	1.82265i	0.0360726	+	0.0624795i
$852$		0			0
$853$	38.5498			1.31992			0.659961	−	0.751300i	$-0.270573\pi$
$853$	38.5498			1.31992			0.659961	+	0.751300i	$0.270573\pi$
$854$		0			0
$855$	−19.6647	+	30.1879i	−0.672520	+	1.03240i
$856$		0			0
$857$	21.0886	−	12.1755i	0.720373	−	0.415908i	−0.0945168	−	0.995523i	$-0.530131\pi$
$857$	21.0886	−	12.1755i	0.720373	−	0.415908i	0.814890	+	0.579616i	$0.196797\pi$
$858$		0			0
$859$	35.0120	+	20.2142i	1.19460	+	0.689700i	0.959345	−	0.282235i	$-0.0910757\pi$
$859$	35.0120	+	20.2142i	1.19460	+	0.689700i	0.235250	+	0.971935i	$0.424409\pi$
$860$		0			0
$861$	−1.05202	+	9.87999i	−0.0358526	+	0.336709i
$862$		0			0
$863$	0.825391	−	1.42962i	0.0280966	−	0.0486648i	−0.851635	−	0.524135i	$-0.824389\pi$
$863$	0.825391	−	1.42962i	0.0280966	−	0.0486648i	0.879732	+	0.475470i	$0.157722\pi$
$864$		0			0
$865$	16.9124	+	29.2931i	0.575038	+	0.995995i
$866$		0			0
$867$	−6.83004	−	12.6005i	−0.231960	−	0.427936i
$868$		0			0
$869$			18.3345i			0.621956i
$870$		0			0
$871$	−27.8248	+	16.0646i	−0.942806	+	0.544329i
$872$		0			0
$873$	−5.80622	−	11.4351i	−0.196511	−	0.387020i
$874$		0			0
$875$	52.2776	−	24.8931i	1.76731	−	0.841539i
$876$		0			0
$877$	5.91238	−	10.2405i	0.199647	−	0.345798i	−0.748767	−	0.662833i	$-0.769354\pi$
$877$	5.91238	−	10.2405i	0.199647	−	0.345798i	0.948414	+	0.317035i	$0.102687\pi$
$878$		0			0
$879$	−19.6437	−	12.0567i	−0.662564	−	0.406662i
$880$		0			0
$881$			22.8739i			0.770642i	0.922783	+	0.385321i	$0.125909\pi$
$881$			22.8739i			0.770642i	−0.922783	+	0.385321i	$0.874091\pi$
$882$		0			0
$883$		−	38.1051i		−	1.28234i	−0.767399	−	0.641170i	$-0.778449\pi$
$883$		−	38.1051i		−	1.28234i	0.767399	−	0.641170i	$-0.221551\pi$
$884$		0			0
$885$	58.9767	+	36.1981i	1.98248	+	1.21679i
$886$		0			0
$887$	−12.8347	+	22.2303i	−0.430947	+	0.746422i	−0.996955	−	0.0779776i	$-0.975154\pi$
$887$	−12.8347	+	22.2303i	−0.430947	+	0.746422i	0.566008	+	0.824400i	$0.308487\pi$
$888$		0			0
$889$	11.4124	−	5.43424i	0.382759	−	0.182258i
$890$		0			0
$891$	−31.5729	−	3.40838i	−1.05773	−	0.114185i
$892$		0			0
$893$	13.0616	−	7.54112i	0.437090	−	0.252354i
$894$		0			0
$895$		−	32.5479i		−	1.08796i
$896$		0			0
$897$	−2.72508	−	5.02742i	−0.0909879	−	0.167861i
$898$		0			0
$899$	−5.89120	−	10.2039i	−0.196482	−	0.340317i
$900$		0			0
$901$	24.2870	−	42.0663i	0.809116	−	1.40143i
$902$		0			0
$903$	0.406242	−	3.81521i	0.0135189	−	0.126962i
$904$		0			0
$905$	51.5657	+	29.7715i	1.71410	+	0.989637i
$906$		0			0
$907$	38.0120	−	21.9463i	1.26217	−	0.728714i	0.288675	−	0.957427i	$-0.406785\pi$
$907$	38.0120	−	21.9463i	1.26217	−	0.728714i	0.973494	+	0.228713i	$0.0734518\pi$
$908$		0			0
$909$	−32.4622	−	21.1463i	−1.07670	−	0.701377i
$910$		0			0
$911$	−17.8693			−0.592037			−0.296018	−	0.955182i	$-0.595659\pi$
$911$	−17.8693			−0.592037			−0.296018	+	0.955182i	$0.595659\pi$
$912$		0			0
$913$	−9.13746	−	15.8265i	−0.302406	−	0.523782i
$914$		0			0
$915$	2.07004	−	76.9804i	0.0684335	−	2.54489i
$916$		0			0
$917$	9.30622	+	0.738558i	0.307318	+	0.0243893i
$918$		0			0
$919$	−30.3625	−	17.5298i	−1.00157	−	0.578255i	−0.0928560	−	0.995680i	$-0.529600\pi$
$919$	−30.3625	−	17.5298i	−1.00157	−	0.578255i	−0.908712	+	0.417424i	$0.862933\pi$
$920$		0			0
$921$	25.5682	+	15.6930i	0.842500	+	0.517101i
$922$		0			0
$923$	−20.7170			−0.681910
$924$		0			0
$925$	−13.4502			−0.442239
$926$		0			0
$927$	0.779542	−	14.4842i	0.0256035	−	0.475725i
$928$		0			0
$929$	5.55082	+	3.20477i	0.182117	+	0.105145i	0.588287	−	0.808652i	$-0.299803\pi$
$929$	5.55082	+	3.20477i	0.182117	+	0.105145i	−0.406170	+	0.913797i	$0.633136\pi$
$930$		0			0
$931$	19.9124	−	7.61369i	0.652602	−	0.249529i
$932$		0			0
$933$	−38.7282	−	1.04142i	−1.26790	−	0.0340946i
$934$		0			0
$935$	−34.9756	−	60.5795i	−1.14382	−	1.98116i
$936$		0			0
$937$	−27.1752			−0.887777			−0.443888	−	0.896082i	$-0.646401\pi$
$937$	−27.1752			−0.887777			−0.443888	+	0.896082i	$0.646401\pi$
$938$		0			0
$939$	−3.67313	−	6.77643i	−0.119868	−	0.221141i
$940$		0			0
$941$	−0.340371	+	0.196514i	−0.0110958	+	0.00640616i	−0.505538	−	0.862805i	$-0.668706\pi$
$941$	−0.340371	+	0.196514i	−0.0110958	+	0.00640616i	0.494442	+	0.869211i	$0.335372\pi$
$942$		0			0
$943$	−3.09967	−	1.78959i	−0.100939	−	0.0582772i
$944$		0			0
$945$	−8.62879	+	53.5207i	−0.280694	+	1.74103i
$946$		0			0
$947$	−6.23157	+	10.7934i	−0.202499	+	0.350738i	−0.949333	−	0.314272i	$-0.898240\pi$
$947$	−6.23157	+	10.7934i	−0.202499	+	0.350738i	0.746834	+	0.665010i	$0.231573\pi$
$948$		0			0
$949$	7.27492	+	12.6005i	0.236154	+	0.409030i
$950$		0			0
$951$	9.30622	−	5.04438i	0.301775	−	0.163575i
$952$		0			0
$953$			60.3290i			1.95425i	0.212670	+	0.977124i	$0.431784\pi$
$953$			60.3290i			1.95425i	−0.212670	+	0.977124i	$0.568216\pi$
$954$		0			0
$955$	63.5619	−	36.6975i	2.05681	−	1.18750i
$956$		0			0
$957$	1.11754	−	41.5589i	0.0361250	−	1.34341i
$958$		0			0
$959$	1.50613	+	1.03659i	0.0486356	+	0.0334733i
$960$		0			0
$961$	−14.0000	+	24.2487i	−0.451613	+	0.782216i
$962$		0			0
$963$	−0.679759	−	0.0365846i	−0.0219049	−	0.00117892i
$964$		0			0
$965$		−	47.7130i		−	1.53593i
$966$		0			0
$967$		−	30.8158i		−	0.990970i	−0.868616	−	0.495485i	$-0.834990\pi$
$967$		−	30.8158i		−	0.990970i	0.868616	−	0.495485i	$-0.165010\pi$
$968$		0			0
$969$	13.8722	−	22.6016i	0.445638	−	0.726067i
$970$		0			0
$971$	13.7735	−	23.8565i	0.442014	−	0.765591i	−0.555825	−	0.831299i	$-0.687597\pi$
$971$	13.7735	−	23.8565i	0.442014	−	0.765591i	0.997839	+	0.0657086i	$0.0209308\pi$
$972$		0			0
$973$	−49.9244	+	23.7725i	−1.60050	+	0.762113i
$974$		0			0
$975$	36.5325	+	0.982378i	1.16998	+	0.0314613i
$976$		0			0
$977$	−24.1633	+	13.9507i	−0.773051	+	0.446321i	−0.833962	−	0.551822i	$-0.813933\pi$
$977$	−24.1633	+	13.9507i	−0.773051	+	0.446321i	0.0609108	+	0.998143i	$0.480599\pi$
$978$		0			0
$979$		−	25.3895i		−	0.811452i
$980$		0			0
$981$	12.8127	−	19.6691i	0.409078	−	0.627987i
$982$		0			0
$983$	16.5901	+	28.7349i	0.529142	+	0.916500i	0.999422	+	0.0339834i	$0.0108193\pi$
$983$	16.5901	+	28.7349i	0.529142	+	0.916500i	−0.470281	+	0.882517i	$0.655847\pi$
$984$		0			0
$985$	35.3746	−	61.2706i	1.12713	−	1.95224i
$986$		0			0
$987$	13.3645	−	18.3421i	0.425395	−	0.583835i
$988$		0			0
$989$	1.19695	+	0.691062i	0.0380609	+	0.0219745i
$990$		0			0
$991$	16.5997	−	9.58382i	0.527306	−	0.304440i	−0.212613	−	0.977137i	$-0.568197\pi$
$991$	16.5997	−	9.58382i	0.527306	−	0.304440i	0.739919	+	0.672696i	$0.234864\pi$
$992$		0			0
$993$	43.0120	−	23.3144i	1.36495	−	0.739861i
$994$		0			0
$995$	83.6113			2.65066
$996$		0			0
$997$	−10.6375	−	18.4246i	−0.336892	−	0.583514i	0.646955	−	0.762528i	$-0.276042\pi$
$997$	−10.6375	−	18.4246i	−0.336892	−	0.583514i	−0.983846	+	0.179015i	$0.942709\pi$
$998$		0			0
$999$	3.76378	−	5.45162i	0.119081	−	0.172482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bj.g.191.3	yes	8
3.2	odd	2	inner	336.2.bj.g.191.4	yes	8
4.3	odd	2		336.2.bj.e.191.2	yes	8
7.2	even	3		2352.2.h.n.2255.6		8
7.4	even	3		336.2.bj.e.95.1	✓	8
7.5	odd	6		2352.2.h.m.2255.3		8
12.11	even	2		336.2.bj.e.191.1	yes	8
21.2	odd	6		2352.2.h.n.2255.4		8
21.5	even	6		2352.2.h.m.2255.5		8
21.11	odd	6		336.2.bj.e.95.2	yes	8
28.11	odd	6	inner	336.2.bj.g.95.4	yes	8
28.19	even	6		2352.2.h.m.2255.6		8
28.23	odd	6		2352.2.h.n.2255.3		8
84.11	even	6	inner	336.2.bj.g.95.3	yes	8
84.23	even	6		2352.2.h.n.2255.5		8
84.47	odd	6		2352.2.h.m.2255.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bj.e.95.1	✓	8	7.4	even	3
336.2.bj.e.95.2	yes	8	21.11	odd	6
336.2.bj.e.191.1	yes	8	12.11	even	2
336.2.bj.e.191.2	yes	8	4.3	odd	2
336.2.bj.g.95.3	yes	8	84.11	even	6	inner
336.2.bj.g.95.4	yes	8	28.11	odd	6	inner
336.2.bj.g.191.3	yes	8	1.1	even	1	trivial
336.2.bj.g.191.4	yes	8	3.2	odd	2	inner
2352.2.h.m.2255.3		8	7.5	odd	6
2352.2.h.m.2255.4		8	84.47	odd	6
2352.2.h.m.2255.5		8	21.5	even	6
2352.2.h.m.2255.6		8	28.19	even	6
2352.2.h.n.2255.3		8	28.23	odd	6
2352.2.h.n.2255.4		8	21.2	odd	6
2352.2.h.n.2255.5		8	84.23	even	6
2352.2.h.n.2255.6		8	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.906034 - 1.47618i) q^{3} +(3.41502 + 1.97166i) q^{5} +(-1.13746 - 2.38876i) q^{7} +(-1.35821 - 2.67493i) q^{9} +O(q^{10})\)	\(q+(0.906034 - 1.47618i) q^{3} +(3.41502 + 1.97166i) q^{5} +(-1.13746 - 2.38876i) q^{7} +(-1.35821 - 2.67493i) q^{9} +(1.76424 + 3.05575i) q^{11} +2.00000 q^{13} +(6.00465 - 3.25479i) q^{15} +(-4.35387 + 2.51371i) q^{17} +(-2.63746 - 1.52274i) q^{19} +(-4.55682 - 0.485208i) q^{21} +(0.825391 - 1.42962i) q^{23} +(5.27492 + 9.13642i) q^{25} +(-5.17926 - 0.418627i) q^{27} -6.80257i q^{29} +(1.50000 - 0.866025i) q^{31} +(6.10930 + 0.164282i) q^{33} +(0.825391 - 10.4004i) q^{35} +(-0.637459 + 1.10411i) q^{37} +(1.81207 - 2.95236i) q^{39} -2.16818i q^{41} +0.837253i q^{43} +(0.635769 - 11.8129i) q^{45} +(-2.47617 + 4.28886i) q^{47} +(-4.41238 + 5.43424i) q^{49} +(-0.234071 + 8.70459i) q^{51} +(-8.36737 + 4.83090i) q^{53} +13.9140i q^{55} +(-4.63746 + 2.51371i) q^{57} +(5.06580 + 8.77423i) q^{59} +(5.63746 - 9.76436i) q^{61} +(-4.84488 + 6.28706i) q^{63} +(6.83004 + 3.94333i) q^{65} +(-13.9124 + 8.03231i) q^{67} +(-1.36254 - 2.51371i) q^{69} -10.3585 q^{71} +(3.63746 + 6.30026i) q^{73} +(18.2662 + 0.491189i) q^{75} +(5.29272 - 7.69014i) q^{77} +(4.50000 + 2.59808i) q^{79} +(-5.31055 + 7.26622i) q^{81} -5.17926 q^{83} -19.8248 q^{85} +(-10.0418 - 6.16335i) q^{87} +(-6.23157 - 3.59780i) q^{89} +(-2.27492 - 4.77753i) q^{91} +(0.0806424 - 2.99892i) q^{93} +(-6.00465 - 10.4004i) q^{95} +4.27492 q^{97} +(5.77774 - 8.86957i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{3} + 6 q^{7} - q^{9}+O(q^{10}) \) 8 * q + 3 * q^3 + 6 * q^7 - q^9	\( 8 q + 3 q^{3} + 6 q^{7} - q^{9} + 16 q^{13} - 6 q^{19} - 19 q^{21} + 12 q^{25} + 12 q^{31} - 11 q^{33} + 10 q^{37} + 6 q^{39} - 17 q^{45} + 10 q^{49} - 9 q^{51} - 22 q^{57} + 30 q^{61} - 27 q^{63} - 66 q^{67} - 26 q^{69} + 14 q^{73} + 66 q^{75} + 36 q^{79} + 7 q^{81} - 68 q^{85} - 54 q^{87} + 12 q^{91} + 3 q^{93} + 4 q^{97}+O(q^{100}) \) 8 * q + 3 * q^3 + 6 * q^7 - q^9 + 16 * q^13 - 6 * q^19 - 19 * q^21 + 12 * q^25 + 12 * q^31 - 11 * q^33 + 10 * q^37 + 6 * q^39 - 17 * q^45 + 10 * q^49 - 9 * q^51 - 22 * q^57 + 30 * q^61 - 27 * q^63 - 66 * q^67 - 26 * q^69 + 14 * q^73 + 66 * q^75 + 36 * q^79 + 7 * q^81 - 68 * q^85 - 54 * q^87 + 12 * q^91 + 3 * q^93 + 4 * q^97

Introduction

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